Yong-Qing Cheng

Algebraic feature extraction for image recognition based on an optimal discriminant criterion

Abstract A novel algebraic feature extraction method for image recognition is presented. The main difference between the present method and any other existing algebraic feature extraction method is that the present method uses an optimal discriminant criterion to extract algebraic features. For the given training image samples, a set of optimal discriminant projection vectors is calculated according to a generalized Fisher criterion function. On the basis of the optimal discriminant projection vector, the projective feature vectors of an image (i.e. algebraic features) are extracted by projecting the image onto all optimal discriminant projection vectors. The method of calculating the set of optimal discriminant projection vectors is discussed. A minimum distance classifier is also proposed for classifying projective feature vectors. Experimental results showed that the present method has good recognition performance. An important conclusion about the present method is that the Foley-Sammon optimal set of discriminant vectors is a special case of the set of optimal discriminant projection vectors.

An efficient algorithm for Foley-Sammon optimal set of discriminant vectors by algebraic method

This paper presents a new method for computing the discriminant vectors of the Foley–Sammon optimal set. First, an equivalent criterion is presented to replace the Fisher criterion; then, the problem of computing the discriminant vectors in Rn is transformed into the maximum problem in a subspace. Several theorems relating to the method are also presented. Experimental results show that the present method is superior to the positive pseudoinverse method, and the perturbation method in terms of correct classification rate.

A generalized optimal set of discriminant vectors

Abstract A generalized optimal set of discriminant vectors for linear feature extraction is presented. First, the criteria of selecting the generalized optimal discriminant vectors are introduced, and then a unified solving method is derived to solve the vectors of the generalized optimal set in both cases of a large number of samples and a small number of samples. The experimental results show that the present method is superior to the Foley-Sammon method (Foley and Sammon, IEEE Trans. Comput. 24, 281–289 (1975)), the positive pseudoinverse method (Tian et al., Opt. Engng 25 (7), 834–839 (1986)), the perturbation method (Hong and Yang, Pattern Recognition 24 , 317–324 (1991)), and the matrix rank decomposition method (Cheng et al., Pattern Recognition 25 , 101–111 (1992)) in terms of correct classification rate.

Human face recognition method based on the statistical model of small sample size

Automatic recognition of human faces is a frontier topic in computer vision. In this paper, a novel recognition approach to human faces is proposed, which is based on the statistical model in the optimal discriminant space. Singular value vector has been proposed to represent algebraic features of images. This kind of feature vector has some important properties of algebraic and geometric invariance, and insensitiveness to noise. Because singular value vector is usually of high dimensionality, and recognition model based on these feature vectors belongs to the problem of small sample size, which has not been solved completely, dimensionality compression of singular value vector is very necessary. In our method, an optimal discriminant transformation is constructed to transform an original space of singular value vector into a new space in which its dimensionality is significantly lower than that in the original space. Finally, a recognition model is established in the new space. Experimental results show that our method has very good recognition performance, and recognition accuracies of 100 percent are obtained for all 64 facial images of 8 classes of human faces.

A robust algebraic method for human face recognition

The feature image and projective image are first proposed to describe the human face, and a new method for human face recognition in which projective images are used for classification is presented. The projective coordinates of projective image on feature images are used as the feature vectors which represent the inherent attributes of human faces. Finally, the feature extraction method of human face images is derived and a hierarchical distance classifier for human face recognition is constructed. The experiments have shown that the recognition method based on the coordinate feature vector is a powerful method for recognizing human face images, and recognition accuracies of 100 percent are obtained for all 64 facial images in eight classes of human faces.<<ETX>>

A novel feature extraction method for image recognition based on similar discriminant function (SDF)

Abstract The extraction of image features is the most fundamental and important problem in image recognition. In this paper, a similarity measure of matrices is first presented, and a similar discriminant function (SDF) of images is established. Based on the discriminant function, we further propose a novel feature extraction method for image recognition. For each class of training image samples, an optimal projection axis maximizing the similarity among these training image samples for the class is calculated. Unlike the common methods of feature extraction, we extract a projective feature vector for a training image sample by projecting the image on the optimal projection axis of the class itself, and a set of projective feature vectors for a testing image sample by projecting the image on all the optimal projection axes. Finally, a hierarchical classifier in the optimal discriminant space is designed to recognize images. In order to test the efficiency of our method, it is used to recognize human faces and English characters. Experimental results have shown that our method has good recognition performance, and the extracted projective feature vectors contain more recognition information than commonly used image features.

Aircraft identification based on the algebraic method

This paper addresses the automatic interpretation of digital image of three-dimensional scenes, especially automatic recognition of three-dimensional aircraft types from digital images. First, an efficient coordinate transform from a series of two-dimensional aircraft posture silhouette images to invariant matrices is developed. The invariant matrix is independent of its translation, scaling, and rotation. Next, on the basis of the invariant matrix, an effective algebraic feature extraction method is proposed. The method is based on singular value decomposition (SVD) of the matrix. To compress the dimensionality of the singular value vector, an optimal discriminant transform for a small number of samples is introduced to transform an original feature space of singular value vector into a new feature space in which its dimensionality is very low. Finally, our method is used to recognize three-dimensional aircraft types Experimental results show that our algebraic method as a high recognition rate, and it is insensitive to translation, scaling, rotation, and noise.

Identification and restoration of images with out-of-focus blurs

This paper presents a new method of identification and restoration of images with out-of-focus blurs. The basic idea of the method is as follows: first use the gradient image of the blur image being processed to estimate the initial value of blur radius; then use the least square restoration technique and the Fibonacci optimal search technique to determine the blur radius. The experimental results with artificially and true defocused images showed that the present method is successful.

Novel approach to human face recognition

This paper presents a new method of human face recognition based on a novel algebraic feature extraction method. An input human face image is First transformed into a standard image; Then, the projective feature vectors of the standard image are extracted by projecting it onto the optimal discriminant projection vectors; Finally, face image recognition is completed by classifying these projective feature vectors. Experimental results showed that the present method is effective.

Calibration of multiple sensors by a planar calibration object

This paper presents an efficient method for calibration of multiple sensors by a planar calibration object. First, a coordinate system PCS is constituted based on the calibration object. Then, the coordinate transformations from the coordinate systems of each camera system and range finder system to PCS are calibrated. By these transformations, the coordinate transformations from one sensor system to the others are calculated.